## Answers to the priming questions

1.) What would happen if these two questions on a recent test of mine were reversed (that is, #4 was given as #5 and #5 was given as #4)?

Sam Alexander essentially got this one right in that students would be more likely to apply a difference of cubes to problem #4. The students would likely pull out a 6x to get $4x^3-1$ and claim the cube root of 4 is 2. As the problem is originally written, the more common issue is to attempt difference of squares instead. It’s possible to do the factoring with difference of cubes if one does not insist the factors are rational (use $4^{\frac{1}{3}}$) but the flat-out mistake is more likely.

2.) The following is a multiple choice question with the image removed. If a student were to ignore the math content of the answers (that is, guess), which would be the most common answer?

The conic section depicted can be categorized as:

a.) Parabola
b.) Ellipse
c.) Cone
d.) Plane
e.) Hyperbola

This answer is nearly creepy, but the sort of thing that happens with priming all the time. Note the strong iteration of a single letter.

The Conic seCtion depiCted Can be Categorized as:

a.) Parabola
b.) Ellipse
c.) Cone
d.) Plane
e.) Hyperbola

Hence the most likely choice by randomness would be C.

EDIT: As adroitly pointed out in the comments the word “cone” is also suggested by the setup word “conic”.

Once you’re aware of priming you will start to notice its effect more often. I stay on the lookout for situations where a student gets a problem wrong not because they didn’t know the mathematics but because they were influenced by the priming in surrounding problems.

### 4 Responses

1. For the conic section problem, I agree – the most likely guess is C. However, it seems to me that is the obvious choice not because of the repetition of the letter C in the problem, but that the problem includes the word “Conic,” which is a derivative of the word “cone.” (Also, at least in my day, I was told to always guess C, as it was the most commonly correct answer.) So, I agree with your conclusion but not your reasoning.

• You’re totally correct about that — that’s an additional bit of priming I forgot to mention even though it was part of the original intent. I’ll add it to the post when I have time. (The way priming works, you can’t say any particular stimulus is the “right” answer, just that the all combine to form a force more or less powerful in influencing a decision.)

• But the C priming doesn’t make any sense:

The Conic seCtion depiCted Can be Categorized as
thE conic sEction dEpictEd can bE catEgorizEd as

Maybe you can argue that the initial Cs are more important as well, but you can’t just say “the Cs prime the C” and not at least call attention to the As, Ds, and Es and offer an explanation for why the Cs prime and the As, Ds, or Es don’t.

• It’s a good point, but hard consonants + initial letters + the word “conic” being the primary object prime stronger.